This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356662 #13 Aug 21 2022 09:26:51 %S A356662 1,4,12,60,240,1740,10080,87360,735840,7514640,79833600,976686480, %T A356662 12454041600,175736040480,2616448554720,42011071502400, %U A356662 711374856192000,12830610027755520,243290200817664000,4870565189425615680,102182981410948838400,2249099140674523737600 %N A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1). %F A356662 a(p) = 2 * p! for prime p. %F A356662 E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k!). %t A356662 a[n_] := n! * DivisorSum[n, 1/(#!)^(n/# - 1) &]; Array[a, 22] (* _Amiram Eldar_, Aug 21 2022 *) %o A356662 (PARI) a(n) = n!*sumdiv(n, d, 1/d!^(n/d-1)); %o A356662 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(1-x^k/k!)))) %Y A356662 Cf. A061095, A098558, A356543, A356661. %K A356662 nonn %O A356662 1,2 %A A356662 _Seiichi Manyama_, Aug 21 2022